Reflections are displayed nicely in preview, but not in final render
This is caused by the simplify option in the scene-tab (at the bottom  of my screenshot).
simply disable it and you're good to go. you can also set the "AO bounces render" to 0 if you want to use other options of the simplifier (simplify subdivisions etc.). This option limits all non-diffuse bounces (0 = no limit)